Introduction to Acoustics

dr inż. Michał Bujacz

[email protected]

Visitng hours: tuesday 15:00-16:00 wednesday 10:00-11:00 „Lodex” 207

Acoustics

[gr.

akoustikós

hearing’] ‘related to field of physics and engineering that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound http://www.physics.byu.edu/ 2

Sound

„

phys.

mechanical disturbance in a compressive medium capable of inducing an auditory sensation, as well as the auditory sensation itself” (Encyklopedia PWN) 3

Longitudinal wave (wzdłużna)

Particles oscillate in the direction of wave propagation. Areas of increased and decreased pressure. What’s the range of movement of the air particles moved by sound ?

0.008nm

t

o 0.1 mm http://www.physics.byu.edu/ 4

Harmonic signal

E

 0 

T x

(

t

) 2

dt P

 1

T

0 

T x

(

t

) 2

dt

Physics vs. perception Physical definitions:

-

Intensity

(natężenie) or amplitude (amplituda)

Psychoacustic definitions:

-

Loudness

(głośność) -

Frequency

(częstotliwość) -

Pitch/tone

(wysokość/ton) -

Tembre

(barwa) -

Spectrum

(widmo) -

Speed

(prędkość) 6

Speed of sound

c



C sztywnosc



gestosc

c = 344 m/s c = 331 + 0,6*T[ o C]

Substance

Carbon Dioxide Oxygen Helium Ethanol Mercury Water Copper Glass Steel

Temperature (°C)

0 0 0 20 20 20 -

Speed (m/s)

259 316 965 1162 1450 1482 5010 5640 5960 7

Intensity of sound

Intensity = the amount of energy passing through an area in time

I



P

4 

r

2  

W m

2  

A

How does amplitude change with distance ?

P

~

E

~

p

2 ~

A

2 ~

I

~ 1

r

2 ~ 1

r

http://hyperphysics.phy-astr.gsu.edu

8

Measures of sound level Pressure

(rms) from 0.00002 N/m2 (threshold of hearing) to 20 N/m (threshold of pain) atmospheric pressure 100000 N/m2 9

Decibel scale

Ratio of power:

L dB

 10 log 10   

P P

0 1    Ratio of amplitude:

L dB L dB

  10 log 10   20 log 10  

A

1 2

A

0 2

A A

1 0     -10 -20 -30 -40

3

0

-3 -6 dB

60 50 40 30 20 10

6 power ratio

1 000 000 100 000 10 000 1 000 100 10 3.98

2

1

0.5

0.251

0.1

0.01

0.001

0.000 1

amplitude ratio

1 000 316.2

100 31.62

10 3.162

2

1.414

1 0.7071

0.5

0.3162

0.1

0.03162

10 0.01

Confusing „sound levels” Sound Power Level (SWL)

- energy emitted by sound source per second (cause)

Sound Pressure Level (SPL)

- pressure (amplitude) changes at receiver (effect)

Sound Intensity Level (SIL)

- energy delivered to receiver area per second (effect)

p

0  20 μPa

P

0  10  12 W m 2 11

http://www.physics.byu.edu/ 12

Loudness

1Fon = 1dBSPL at 1kHz 13

Frequency

14

Audio frequency ranges Tones

Low bass : 20 – 80 Hz Upper bass : 80 – 320 Hz Lower mid : 320 – 2560 Hz Upper mid : 2560 – 5120 Hz High/treble : 5120 Hz – 20000 Hz

Examples

Lowest two octaves.

Explosions, storms, lowest church organ notes 3 th – 4 th o ctaves Drums, bass, cellos, wind instruments 5 th – 7 th o ctaves Most instruments and human speech 8 th o ctave Highest notes on most instruments, whistles, most sensitive perception range 9 th 10 th octave Percussion (hi-hat, cymbal), higher harmonics of sounds, noise 15

Human perception

16

Musical tone (pitch)

Musical scales – divided into octaves (intervals), e.g. C (dur) A 4 = 440Hz Psychoacoustic scales – Mel or Bark 17 http://www.sfu.ca/

Freq. components

18

Fourier transform

19

Spectrum of a sound

20

Real spectrum

Częstotliwość (Hz) 21

Cutting the spectrum into octaves

22

Tembre/quality

Set of features distinguishing sounds of the same base frequency on different instruments Spectrum dependent (harmonics and noise) and transients (sudden changes) Described semantically (np.brightness, warmth, coarsness, clarity) 23

Sound envelope

24

Anatomy of hearing

25

Cochlea

26

Future topics

Psychoacoustics Spatial audio Room acoustics (wave phenomena) Spectrum analysis (Fourerier, DFT, FFT) Noise and sound standards Math of Music Electroacoustics Studio equipment Sound synthesis Speech signals Speaker sets 27